~~ time. The most common method of specifying a frequency is in terms of vibrations per second. Frequency is measured in
I"""] units of hertz, abbreviated Hz.
The frequency of a sound is interpreted by your ear as a pitch. Faster rates of vibration produce higher pitches. Usually, f"j the smaller an instrument, the higher the pitch it can produce.
~~ A piccolo can produce a very high pitch, whereas a tuba pro duces a very low pitch.
f""| Although the human ear can detect a wide range of fre-quencies, only frequencies occurring at specific intervals are
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commonly used in music. Let's start with one of these pitches and label it C. This pitch has a frequency of 261.63 Hz, or 261.63 vibrations per second. The sequence of pitches contin ues, with pitches at the following intervals being named D, E, F, G, A, and B.
B 493.88 Hz A 440.00 Hz G 392.00 Hz F 349.23 Hz E 329.63 Hz D 293.66 Hz
C 261.63 Hz (Start here)
When you listen to the sequence of pitches in order, they form a scale, but the scale wilt seem incomplete. One final note, after the B, is needed to complete the scale. This note happens to be another C, related to the earlier C, but at a higher pitch. (The actual mathematical relationship is that the new C occurs at 523.25 Hz, exactly twice the frequency of the first.) It doesn't stop here, though. There's another D after the new C, and a second E after the new D, and so on. In fact, the scale repeats several times, both above and below the original C.
D 1174.70 Hz C 1046.50 Hz B 987.77 Hz A 880.00 Hz G 783.99 Hz F 698.46 Hz E 659.26 Hz D 587.33 Hz C 523.25 Hz B 493.88 Hz
A. 440.00 Hz i )
G 392.00 Hz LJ
F 349.23 Hz E 329.63 Hz
D 293.66 Hz M
C. 261.63 Hz (Original C) B 246.94 Hz
A 220.00 Hz J I
G 196.00 Hz LJ
LJ
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F 174.61 Hz E 164.81 Hz D 146.83 Hz C3 130.81 Hz B 123.47 Hz
The scale repeats with each C. By examining one se quence, from one C to the next, you can see that it consists of eight pitches. Collectively, these eight pitches are called an oc tave. To distinguish this set of pitches from the next, the first set is said to occur one octave lower than the second.
Just as the different pitches in an octave are labeled, so are the different octaves. However, instead of using a letter of the alphabet, a number is used. The piano key for the original C is found at about the middle of the keyboard. This C is called middle C, and begins octave 4. Other octaves are num bered relative to the octave containing middle C. The octave immediately above octave 4 is octave 5. The octaves which are of the most use musically are octaves 1-7.
In music notation, the pitch value of a note is represented by its vertical position when drawn on a staff. Thus, C5 (C of the fifth octave) is indicated by placing the note between the second and third lines of the treble staff. The next higher pitch, D5, is indicated by placing the note above the position for C5, except this time the note is placed on the line. For the entire grand staff, the positions for all notes alternate between being on a staff line or between staff lines. See Figure 5-3 for an illustration.
Middle C is a special case. The staff line for C4 is placed halfway between the treble and bass staves. The pitches around middle C must take this variation into account. The separation of the two staves creates some space used for mes sages and special symbols which give additional information to the performer.
Another special situation is when a note is so high or low in pitch that it goes off the grand staff. In such instances, addi tional staff lines, called leger lines (see Figure 5-4), are added.
t-m The pitch of notes drawn on leger lines is still determined in I J the normal way, by counting staff lines and seeing whether
the note is placed on or between lines.
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Figure 5-4. Leger Lines
G F E D C
B C
By using the grand staff and leger lines, eight octaves (oc taves 0-7) can be displayed.
Sharps and flats. Eight octaves, each containing 7 differ ent pitches, would seem to make a total of 56 pitches. Actu ally, there are some intermediate pitches between some of these notes. These are called sharps and flats.
C B
A-sharp B-flat A
G-sharp A-flat G
F-sharp G-flat F
E
D-sharp E-flat D
C-sharp D-flat C
A note is sharp if its pitch is a half step above normal. A note is flat if the pitch is a half step below the normal pitch.
Notes that are not sharp nor flat are said to be natural Figure 5-5 shows some of the natural notes on the piano keyboard.
Figure 5-5. Piano Keyboard
A \B F\ C
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Two important observations should be made. First, every sharp note is equivalent to a flat note. C-sharp and D-flat both denote the same pitch. The difference lies in the viewpoint, whether the intermediate pitch is a half step above C or a half step below D.
Thus far, we've been using the words sharp and flat for accidental pitches. Another way to indicate that a note is sharp or flat is to use a special symbol. The symbol for a sharp note looks like a slanted pound sign (#), while the symbol for a flat note looks something like a lowercase letter B (\>). the natural symbol is normally not used in front of natural notes.
To show that a note on the grand staff is a sharp or flat note, the appropriate accidental symbol is placed just before the note. The C-sharp and B-flat notes in Figure 5-6 are signi fied with these symbols. Sharps and flats indicated in this way last only one measure.
Figure 5-6. Accidentals
C C-sharp D E C B B-flat A
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Including the sharps and flats, one octave consists of 12 different pitches. With eight octaves, the total is now 96 differ ent pitches. Most songs use only notes that come from this palette of 96 pitches.
Key signatures. Just because there are 96 pitches avail able, does that mean that each one will be used in a song? No,
a song may not play in every octave, nor every note within a ) j particular octave. Perhaps it uses just a subset of the 12
pitches within one octave. The selection of notes is determined
by the key in which the music is written. j j
The topic of pitch was introduced by starting with a C scale. This is a sequence of notes, starting on C, that continue
for one octave. Let's examine the relationship of these notes to jl the 12 in the entire octave. If the distance between each of the
12 pitches is called a half step, the sequence of notes forming
the C scale is determined by the following steps: whole, j|
whole, half, whole, whole, whole, half—where a whole step equals two half steps.
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cB
a#/bI>
fH/gI>
f E
Now apply that sequence of steps again, but this time start the scale at note A.
A
Git
FjtE DCtf
B
A (Start here)
This scale contains three sharp notes, as opposed to the earlier scale which contained none. The sharp notes replaced their natural counterparts. This scale is said to be written in the key of A. A song written in the key of A will normally use only this set of pitches in each octave. This means that we're back to a situation where we have to deal with only seven pitches per octave.
You can start a scale on any note, and for every starting note, there is a different combination of sharp or flat notes used. Here's another example, this time using flats:
m Bb (Start here)
' ' This is the key of B-flat. The notes were determined by using the sequence of half and whole steps given earlier. The
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key of B-flat contains two flat notes, B-flat and E-flat. The notes B-natural and E-natural will not normally be used by a song written in the key of B-flat.
Table 5-1 is a complete listing of all the major keys. The keys with less than five sharps or flats are the ones used most often. If you study Table 5-1 carefully, you'll notice some pat terns. For example, each key which contains sharp notes con tains F#. The key of G has F# as its only sharp note. The key of D keeps the F#, but adds C#. Each successive key adds one more sharp note, while retaining all the other sharp notes from before. This pattern works in the same way for keys con taining flat notes, starting with the note Bb.
Most of the time you can determine the key in which a piece of music is written by counting the number of sharp or flat symbols near the clef symbols on the grand staff. If no sharp or flat symbols appear there, the music is written in the key of C. If one sharp symbol is displayed, the piece is written in the key of G. Two sharp symbols mean that the key of D is to be used, and so on. Likewise, one flat symbol indicates the key of F, two indicate the key of B-flat, on up to seven flat symbols, which indicate the key of C-flat.
Just as the number of sharp or flat symbols is important, so is their position. The sharp symbol for F# is always placed
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f-*> on the line that designates note F. Furthermore, when a sharp
! ^ symbol is put next to the clef symbol, it has the effect of auto matically placing a sharp symbol in front of every note on that r—> line. A sharp Symbol on line F means that all notes placed on
- J the grand staff in F positions are to be played as F-sharps. Of
course, the same is true when flats are used. A flat symbol r—> placed near the clef on the line for B means that all B notes ' s should be played as B-flats.
Sharp and flat symbols placed after a clef symbol are called a key signature. The use of a key signature saves a lot of work when writing music, because it's no longer necessary to write a sharp or flat symbol in front of every note that needs one.
Figure 5-7 contains some examples of key signatures.
Since all keys that contain sharps contain F#, all of these keys have a sharp symbol at the F position. Each successive key adds a sharp symbol at a new position while retaining all the old ones. Also notice that a sharp or flat on one line affects not only the notes on that line, but the corresponding notes in the octaves above and below as well.
Duration. The vertical position of a note on the grand staff determines its pitch. The horizontal direction of the staff indicates time. A sequence of notes is played in order from left to right, just as text is read from left to right. By putting the pitches together in a pleasing order, you'll create a melody, the basis for a song.
Pitch, however, is only one major characteristic of a note.
Another important quality of a note is its duration. In a song, notes are not always played at the rate of one note every beat.
Sometimes a note may be played for two beats. Other times, two notes might be played within the span of one beat,
mean-<—» ing that each note is half a beat long. Thus, every note on the 1 N staff is going to have to specify not only its pitch, but also its
duration in terms of beats.
r—j The duration of a note is indicated by its shape. The
stan-[. ^ dard note you've been using thus far is formally called a quar
ter note, and is drawn with a stem and a filled-in oval at the r—^ bottom. If we assume a quarter note plays for a duration of one